Kasso A. Okoudjou, "A Beurling-Helson type theorem for modulation spaces", Journal of Function Spaces, vol. 7, Article ID 956891, 9 pages, 2009. https://doi.org/10.1155/2009/956891
A Beurling-Helson type theorem for modulation spaces
We prove a Beurling-Helson type theorem on modulation spaces. More precisely, we show that the only 𝒞1 changes of variables that leave invariant the modulation spaces ℳp,q(ℝd) are affine functions on ℝd. A special case of our result involving the Sjöstrand algebra was considered earlier by A. Boulkhemair.
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